This article presents a hierarchical control framework that integrates predefined-time convergence and adaptive compliance control to achieve robust and stable quadruped locomotion over complex and irregular terrains. The proposed framework addresses the challenges posed by terrain uncertainties and dynamic interactions during locomotion. Specifically, a predefined-time nonsingular fast terminal sliding mode controller (PTNFTSMC) is developed for the swing phase to ensure fast and accurate trajectory tracking within a predefined time bound, while avoiding singularities and being independent of initial conditions. For the stance phase, a disturbance-aware adaptive impedance controller is proposed, which enables real-time stiffness estimation and damping adjustment based on variations in contact forces, thereby improving ground contact stability and enhancing terrain adaptability. A unified Lyapunov-based theoretical framework is employed to guarantee global predefined-time stability across all gait phases, ensuring reliable performance even in uncertain environments. The effectiveness and robustness of the proposed control strategy are validated through extensive simulations and real-world hardware experiments. The results demonstrate that the proposed approach significantly improves tracking accuracy, reduces convergence time, and enhances the quadruped robot's ability to maintain stable locomotion under various terrain conditions and external disturbances.
Xu et al. (Sun,) studied this question.